Proximal Point Method Involving Hybrid Iteration for Solving Convex Minimization Problem and Common Fixed Point Problem in Non-positive Curvature Metric Spaces

2018 ◽  
pp. 201-214
Author(s):  
Plern Saipara ◽  
Kamonrat Sombut ◽  
Nuttapol Pakkaranang
Keyword(s):  
Fixed Point ◽  
Minimization Problem ◽  
Metric Spaces ◽  
Positive Curvature ◽  
Fixed Point Problem ◽  
Convex Minimization ◽  
Proximal Point Method ◽  
Point Problem ◽  
Proximal Point ◽  
Common Fixed Point Problem

scholarly journals Common Fixed Point for Two Pairs of Mappings Satisfying (E.A) Property in Generalized Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Wei Long ◽  
Mujahid Abbas ◽  
Talat Nazir ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Common Fixed Point Problem

Recently, Abbas et al. (2012) obtained some unique common fixed-point results for a pair of mappings satisfying (E.A) property under certain generalized strict contractive conditions in the framework of a generalized metric space. In this paper, we present common coincidence and common fixed points of two pairs of mappings when only one pair satisfies (E.A) property in the setup of generalized metric spaces. We present some examples to support our results. We also study well-posedness of common fixed-point problem.

scholarly journals New Existence Results for Fixed Point Problem and Minimization Problem in Compact Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Weng-Seng Heng ◽  
Wei-Shih Du ◽  
Chi-Lin Yen
Keyword(s):  
Fixed Point ◽  
Minimization Problem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Theorems ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Convexity Property ◽  
Linear Spaces ◽  
Compact Metric Spaces

We first present some new existence theorems for fixed point problem and minimization problem in compact metric spaces without assuming that mappings possess convexity property. Some applications of our results to new fixed point theorems for nonself mappings in the setting of strictly convex normed linear spaces and usual metric spaces are also given.

scholarly journals Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 158
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Boundary Value ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Existence Of A Solution ◽  
Shadowing Property ◽  
Limit Shadowing ◽  
Type Boundary ◽  
Cyclic Type

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

scholarly journals An alternating iteration algorithm for solving the split equality fixed point problem with L-Lipschitz and quasi-pseudo-contractive mappings

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Meixia Li ◽  
Xueling Zhou ◽  
Haitao Che
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Split Feasibility Problem ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Iteration Algorithm ◽  
Point Problem ◽  
Contractive Mappings ◽  
Common Fixed Point Problem ◽  
Significant Generalization

Abstract In this paper, we are concerned with the split equality common fixed point problem. It is a significant generalization of the split feasibility problem, which can be used in various disciplines, such as medicine, military and biology, etc. We propose an alternating iteration algorithm for solving the split equality common fixed point problem with L-Lipschitz and quasi-pseudo-contractive mappings and prove that the sequence generated by the algorithm converges weakly to the solution of this problem. Finally, some numerical results are shown to confirm the feasibility and efficiency of the proposed algorithm.

scholarly journals A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 372
Author(s):  
Nishu Gupta ◽  
Mihai Postolache ◽  
Ashish Nandal ◽  
Renu Chugh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Prior Knowledge ◽  
Iterative Algorithm ◽  
Fixed Point Problem ◽  
Null Point ◽  
Operator Norm ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.

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